A Modern Approach to Quantum Mechanics · Problem 12.4

Scattering — John S. Townsend

Physics — Quantum Mechanics · variational-method-anharmonic-oscillator

Problem

Use the variational principle to estimate the ground-state energy for the one-dimensional anharmonic oscillator

\hat{H} = \frac{\hat{p}_x^2}{2m} + b\hat{x}^4

Compare your result with the exact result

E_0 = 1.060 b^{1/3} \left(\frac{\hbar^2}{2m}\right)^{2/3}